An unequal trapezoid is given. top base – 20 bottom base – 60 right side – 37 left side – 13

| August 2, 2021 | education

An unequal trapezoid is given. top base – 20 bottom base – 60 right side – 37 left side – 13 Find the area of the unequal trapezoid.

Let us lower two heights from the top of C and B to the base of the trapezoid AD BK = CH, as the heights of the trapezoid.

Let the segment DH = X cm, then AK = (40 – X).

In a right-angled triangle CHD, by the Pythagorean theorem CH ^ 2 = CD ^ 2 – X ^ 2 = 37 ^ 2 – X ^ 2.

In a right-angled triangle ABK, according to the Pythagorean theorem, BK ^ 2 = AB ^ 2 – (40 – X) ^ 2 = 132 – (40 – X) ^ 2.

Since CH = BK, then:

37 ^ 2 – X ^ 2 = 13 ^ 2 – (40 – X) ^ 2.

1369 – X ^ 2 = 169 – (1600 – 80 * X + X ^ 2).

1369 + 1600 – 169 = 80 * H.

2800 = 80 * H.

X = 35 cm.

НD = 35 cm.

Then CH ^ 2 = 37 ^ 2 – 35 ^ 2 = 1369 – 1225 = 144.

CH = 12 cm.

Then the area of the trapezoid is:

S = AD * CH = 40 * 12 = 480 cm2.

S = 480 cm2.

Answer: The area of the trapezoid is 480 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.